Legal Question in Landlord & Tenant Law in New York

I assume he paid rent six months ago, so he's not a squatter, but a tenant.

You should serve him with a full month's notice to quit. That means if you give notice now it will speak as of September 1 and require him to remove by September 30. Then you have a holdover proceeding. It may still take until the end of the year to get the freeloader out, but he will have to move.

You could try to remove him sooner, but the odds are that you will lose and it will end up taking longer to get him out. You could also try to do a non-payment proceeding, which could be started in four days' time, but the surest way is a holdover proceeding. I would also send notice by hand delivery and certified mail making it clear that he will need to find a new place to live by October 1.